Geometric actions and flat space holography

Merbis, Wout; Riegler, Max

doi:10.1007/JHEP02(2020)125

Geometric actions and flat space holography

Wout Merbis
(
- Brussels U., PTM and
- Intl. Solvay Inst., Brussels
)
,
Max Riegler
(
- Harvard U.
)

Dec 17, 2019

61 pages

Published in:

JHEP 02 (2020) 125

Published: Feb 21, 2020

e-Print:

1912.08207 [hep-th]

DOI:

10.1007/JHEP02(2020)125

View in:

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Abstract: (Springer)

In this paper we perform the Hamiltonian reduction of the action for three- dimensional Einstein gravity with vanishing cosmological constant using the Chern-Simons formulation and Bondi-van der Burg-Metzner-Sachs (BMS) boundary conditions. An equivalent formulation of the boundary action is the geometric action on BMS

_{3}

coad- joint orbits, where the orbit representative is identified as the bulk holonomy. We use this reduced action to compute one-loop contributions to the torus partition function of all BMS

_{3}

descendants of Minkowski spacetime and cosmological solutions in flat space. We then consider Wilson lines in the ISO(2, 1) Chern-Simons theory with endpoints on the boundary, whose reduction to the boundary theory gives a bilocal operator. We use the expectation values and two-point correlation functions of these bilocal operators to compute quantum contributions to the entanglement entropy of a single interval for BMS

_{3}

invariant field theories and BMS3 blocks, respectively. While semi-classically the BMS

_{3}

boundary theory has central charges c

_{1}

= 0 and c

_{2}

= 3/G

_{N}

, we find that quantum corrections in flat space do not renormalize G

_{N}

, but rather lead to a non-zero c

_{1}

.

Note:

61 pages, v2: typo's fixed and ref's added, v3: added comments and improved discussions. Matches version accepted for publication in JHEP

Gauge-gravity correspondence
Chern-Simons Theories
Field Theories in Lower Dimensions
Conformal and W Symmetry
partition function: torus
cosmological constant: 0
space-time: Minkowski
entropy: entanglement
correction: quantum
dimension: 3

References(136)

Figures(0)

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